1. Field of the Invention
Retro reflectors for electromagnetic waves, acoustic waves, and other wave phenomena have been known since the Fessenden patent (1,384,014) in 1921. These devices reflect the wave energy preferentially in the direction back toward the source. This creates a much stronger reflection of energy back toward the source than would occur if the reflection were to be equally strong in all directions.
2. Description of the Related Art
A retro reflector is a device which generally produces a strong return in the direction of the source, while the strength of this return may depend on the orientation of the reflector. The Luneberg Lens is completely insensitive to the direction of incidence of the waves. This is often a desirable property. However, the Luneberg Lens is unsuitable for many applications for reasons such as cost and weight. Cost and weight are also a limitation for the Van Atta Array, which generally is sensitive to the direction of incidence.
An alternative which is often cheaper to build and lighter in weight is a corner reflector consisting of two or three substantially perpendicular surfaces, similar to those used in the Fessenden patent. Retro reflectors may also consist of an array of corner reflectors, each oriented differently. These retro reflectors have received much attention. They originally were used primarily for radar and more recently have become especially important also for light such as from lasers. They are also useful for sonar. However, in prior art they generally have had a significant limitation. While they give a strong return towards the source over many or most incident directions of the waves, they generally give a weak return over some ranges of incident directions. This can be a significant limitation. For example, small boats often use radar reflectors so that they can be seen on a large ship""s radar in foggy conditions. This is an aid in preventing collisions. However, if there are certain directions where the backscattered return is weak, then for ships approaching from these directions they might not be seen from a distance and a collision might occur.
The importance of a uniformly strong backscattered return for all (or for a large range of) incidence angles has been widely recognized. Boating magazines and the sales literature for radar reflectors for small boats have often included graphs of this strength for several commercially available radar reflectors from different manufacturers. One set of test results that is often quoted is the Admiralty Surface Weapons Establishment tests from England.
Test results have shown again and again that a corner formed by three mutually perpendicular reflecting surfaces gives an effective retro reflector. It produces a very strong return for all incidence angles which look into the corner and which see a significant area for all three surfaces. However, there are some incidence directions which see the interior of a corner, while this incidence direction is also nearly parallel to one of the three surfaces. That is, for these directions the projected area of that one surface (projected onto a plane perpendicular to the incidence direction) is very small. In this case, when looked at from the source, one of the surfaces of the retro reflector is viewed nearly end on. For these directions, the retro return may not be strong. This results in a serious limitation in prior art.
Often, an array of retro reflectors is formed by three perpendicular (or nearly perpendicular) intersecting reflecting surfaces, where each surface continues past the line of intersection. This produces eight interior corners, each of which functions as a retro reflector for some angles of incidence. We will call this the standard array of corner reflectors. FIG. 1 gives an example of the standard array of corner reflectors. Four of the interior corners are visible in FIG. 1 and there are four more corners which are not visible in this view.
The standard array of corner reflectors has a significant limitation. For waves incident in a direction nearly parallel to any one of its surfaces, the retro return may be small. For some applications using the standard array, the directions of incidence that are important are all substantially horizontal directions. For example, for a boat in conditions of limited visibility it is important to appear on the radar of other boat and ships. When the standard array is used, it may be oriented in different ways. The orientation has a significant affect on the strength of the retro-return. The orientation with one surface horizontal and two surfaces vertical will be called the xe2x80x9cspill waterxe2x80x9d orientation. The orientation with one corner pointed upwards will be called the xe2x80x9chold waterxe2x80x9d position. The hold water orientation is illustrated in FIG. 1. In this orientation, one might think of the upper corner as holding water that is poured into it. This language will be used even though the surfaces of the retro reflector might not contain water. For example, they may have large holes or they may be made from a mesh or a porous material. The hold water orientation is often considered as the preferred orientation. For incidence from substantially horizontal directions, it is less likely that a direction of an incident source will be nearly parallel to one of its surfaces than for the spill water orientation. However, for some horizontal directions this does still occur.
The importance of producing a large retro return in all directions has led to attempts to xe2x80x9cfinessexe2x80x9d the problems that a non omnidirectional retro reflector creates. For example, a retro reflector can be made to spin. Two examples of this are given in the Norwood Patent (#2,746,035) and the Matson patent (#2,702,900).
There have been many attempts at making the return of a retro reflector more even as a function of the incident direction. Taking just one example of many, the Aw Patent (#5,097,265) describes an array of twenty corner reflectors (twenty interior corners). It is possible to arrange an array of reflectors by the xe2x80x9cAwxe2x80x9d method or by many other methods so that for all angles of incidence there is at least one corner reflector such that its interior and all three of its interior surfaces can be seen. However, this is not sufficient to ensure a strong retro return for all angles of incidence. Wave phenomena involve interference effects. The return from two or more corner reflectors may interfere constructively or destructively. Destructive interference can cause two returns to cancel or to nearly cancel each other, resulting in a very weak total return.
One might also attempt to make the return more even as a function of incidence direction by use a large number (in some cases as large a number as twenty or more) of corner reflectors all oriented differently. Certain theorems in statistics, related to the central limit theorem, then suggest the properties that result. It is unlikely that destructive interference would give a very weak return for any angle of incidence. However, this method generally produces a somewhat uniform return for all angles, which is uniformly moderate, not strong and not weak.
The amount of energy returned to the source by a retro reflector depends on many factors, such as the design and orientation of the reflector, the distance to the source, and the strength of the source. In some cases polarization also matters. If all of these factors are kept constant, then the energy returned will increase as a larger retro reflector is used. The amount of energy that a retro reflector intercepts will be proportional to the square of its linear dimension. However, for a well designed retro reflector the amount of energy returned to the source will be approximately proportional to the fourth power of its linear dimension. The reason for this is that larger retro reflectors direct the reflected energy into a narrower beam. This beam is narrower in both directions transverse to the direction of propagation. Thus, for larger retro reflectors more energy is reflected and also a larger fraction of the reflected energy will hit the source.
Three properties can be identified as desirable for a retro reflector made from an array of corner reflectors. First, a few large corner reflectors are better than many small corner reflectors. This follows from the fact that, for one corner and for incidence towards the interior of that corner, the strength of the retro-return is approximately proportional to the fourth power of the linear size of the corner. Second, for all incidence angles that are of interest, at least one (or more) corner should be oriented to produce a large return. Third, if more than one corner reflector produces a large return for some incidence angle, then these returns should be substantially in phase. This will ensure constructive interference.
These properties are not absolute. In part, they are based on xe2x80x9chigh frequencyxe2x80x9d approximations which describe wave phenomena. The term xe2x80x9chigh frequencyxe2x80x9d means that these approximations become more accurate when physical dimensions become much larger than a wavelength. Also, there are other important properties which have not been mentioned. However, the three properties identified above may be a useful aid in understanding some of the important differences between the present invention and prior art.
For scattering of waves such as sound or electromagnetic radiation, including but not limited to radar, light and sonar, the wave has both a magnitude and a phase. For two waves to interfere constructively, their phases need to be substantially equal. If their phases are approximately opposite, then they interfere destructively. To insure a strong return from a retro reflector, it is desirable that when the interiors of two corners are both visible from some direction the returns from these two corners interfere constructively. A sufficient condition to ensure this is that the round trip path lengths for reflection from these two corners do not differ by more than a quarter of a wavelength.
The reflection off each of the three sides of a corner may be described approximately by the condition that the angle of incidence equals the angle of reflection. The corner is generally constructed with these three sides approximately perpendicular to each other. A ray incident towards the interior of a corner reflects off all three sides of the corner and then is directed back towards the source of that ray. As an example, one of the corners in FIG. 1 is formed by the three sides 101, 102, and 103. The word xe2x80x9crayxe2x80x9d is related to a high frequency approximation, which is useful for understanding approximations to how a retro reflector behaves. Each of the various possible ray paths results in the same total distance traveled (assuming parallel rays incident from a distant source). For different ray paths the ray bounces off different parts of the sides of the corner and may also reflect off the successive sides in different orders. The distance traveled for any of these rays is the same as for a ray which goes to the interior vertex 104, and then reverses direction. The term interior vertex is defined to be the point where the three sides of a corner meet.
The path length traveled for any of the rays reflected from the three sides of a corner may be described by the location of the corner""s interior vertex. If radiation were incident from a substantially horizontal direction, and two different corners were to have vertices located one above the other, then the total path lengths for both corners would also be approximately the same. This would result in constructive interference.
The standard array in hold water orientation has eight corners. One is on the top, and one is on the bottom. The remaining six are on the sides. In FIG. 1 the corner on the top has the three sides 105, 106, and 107. A limitation of this array is that as one looks at it substantially horizontally from various azimuthal directions, there are six such directions in which there is no corner with its interior visible. These are directions which look along one of the surfaces, and the interior of that surface is not visible. For example, one of these directions would be for a source in the plane containing the surface 102. For many directions near these six directions, the retro return may be small.
This invention consists of more than one corner, in a novel arrangement. This invention can be applied using two or more corners. For example, it may be applied using six corners. However, their orientation and placement will be different than as in the standard array. We define the lower three corners as those corners where two sides meet in a line along their upper portion. The corner formed by sides 101, 102, and 103 is a lower corner. Sides 101 and 102 meet along the line 108. The lower corners have one side along their bottom, such as side 103 which has an edge 105. The three upper corners have two sides meeting along their lower portion, and one side along their upper portion. The corner formed by sides 106, 109, and 101 is an upper corner. Sides 109 and 101 meet along the line 110.
The lower three corners might be rotated so that they face more upwards, while the three upper corners might be rotated so that they face lower, as compared to their orientation in the standard array. As viewed from the side, this results in the corners becoming more xe2x80x9copenxe2x80x9d in the sense that when viewed from the side more interior area may be seen. This rotation will be called an opening rotation. For the lower corner formed by 101, 102, and 103, this rotation is about an axis parallel to the line 105. When viewed from the right end of line 105 (the end that intersects side 102), the opening rotation is a clockwise rotation.
In performing this rotation, the sizes of the faces of the corners may also be modified by xe2x80x9ctrimmingxe2x80x9d so as to make the array fit together better. Also, for example, if a wire mesh is used for the surfaces, then as an option the surfaces of the corners might be permitted to penetrate through each other to some extent. In addition, the corners may be translated (moved without rotation) to help them to fit together.
A smaller number of corners can also be used. For example, two successive corners might be used, with an opening rotation for one or both. The arrangement of corners described here allows the interior of at least one corner to be visible from every incident direction in some range of interest. For example, one corner might be visible from every substantially horizontal incident direction. This is a result of the opening rotation, which is one feature distinguishing this invention from the standard array. This new arrangement also provides that when the interiors of two corners are visible at the same time, the path length for both corners is generally approximately equal. In one embodiment it is approximately equal because the vertices of these two corners are displaced substantially vertically, and the incidence direction is substantially horizontal. In other embodiments there is a horizontal displacement which is small. Also, in some embodiments this arrangement provides that an approximately vertical displacement between interior vertices is small. Since it is small, the difference in the two path lengths traveled is relatively insensitive to small changes in the orientation of the array or small changes from horizontal incidence. This is especially useful when used on a sailboat which may be healing to one side. As the opening rotation is made larger, this difference in path lengths generally grows larger. It is thus desirable minimize the size of the opening rotation. More generally, by minimizing the opening rotation the interior corners of different corners may be kept spatially close to each other which permits a variety of orientations with the path lengths approximately equal.
There are two important results of an opening rotation. Both of these results were discussed above, but it is worth repeating them. First, for many incident directions of interest for a ray, the three sides are presented more evenly to that ray. This generally results in a larger retro return from that one corner. These directions of interest are often have a large horizontal component and a relatively small vertical component. Second, for such directions the range of azimuthal directions that look into the interior of one corner is larger. For example, for horizontal incidence and the standard array in hold water orientation, the interior of one corner may be seen over sixty degrees of azimuth. An opening rotation increases this to greater than sixty degrees.
Using the language of a ray approximation, one mechanism for a corner to give a relatively strong reflection in the retro direction is three reflections, one from each interior face. The term trihedral return is defined to be this relatively strong reflection in the retro direction. This trihedral return is associated with the aspect angles for which this return is relatively strong. For example, using the lower corner in FIG. 1, the trihedral return would involve reflections off of sides 101, 102, and 103 in any order. For an incident ray nearly parallel to one of the three faces, there can also be a relatively strong return after two reflections, one off of each of the other two faces. The term dihedral return is defined to be this relatively strong reflection in the retro direction after two reflections. This dihedral return is associated with the aspect angles for which this return is relatively strong. For example, again using the lower corner of FIG. 1, an incident ray might be approximately in the plane of side 102. A dihedral return would involve that ray bouncing off of sides 101 and 103 in either order.
For an incident ray very nearly in the plane of surface 102, the dihedral return may be strong. However, for small changes in the incident direction the dihedral return may not be strong. For one corner, there generally is a range of incident directions, between those where the trihedral return for a corner is strong and where the dihedral return for that corner is strong. This is an angular region where the retro-return is relatively weak. It is possible to choose an opening rotation such that the dihedral return from one corner is located in the angular region between the trihedral and dihedral returns from another corner. This results in the total return being relatively uniform in angle, since it eliminates the null which would otherwise be present between the trihedral and dihedral returns for that other corner. This is a desirable method since it only requires a relatively small opening rotation. For example, a much larger opening rotation would be required to eliminate the null by making the trihedral return from one corner overlap the trihedral return from another corner.
This invention involves an array of two or more corner reflectors, with opening rotations and with translations of the individual corner reflectors. These are chosen to produce a strong retro-return and/or a substantially uniform retro-return over a desired range of angles.